Hamming graphs in Nomura algebras

Let A be an association scheme on q≥3 vertices. We show that the Bose–Mesner algebra of the generalized Hamming scheme H(n,A), for n⩾2, is not the Nomura algebra of any type II matrix.This result gives examples of formally self-dual Bose–Mesner algebras that are not the Nomura algebras of type II matrices.